Optimization of Shell and Truss Structures based on Size and Shape Parameterization

Authors:

Arnout, Saartje; M0319233

Issue Date:

30-Aug-2012

Abstract:

During the design process, structural optimization is a powerful tool to obtain new and well performing designs. In this work, structural optimization is studied for shell and truss structures. Both structural typologies appear frequently in contemporary architecture. Since the structural behavior of shells is strongly influenced by the geometry, optimization is an essential part of shell design. Shells are often designedas double curved space trusses with a continuous covering. In addition,many benchmark problems in structural optimization are defined for trusses, due to the simplicity of their structural analysis.The aim of the optimization is to change the geometry of the structure such thatthe material use is reduced as much as possible, while still satisfyingthe safety and serviceability requirements as prescribed by the Eurocode. The optimization problem is formulated for shells and trusses. The specific design variables, objective and constraint functions are described in detail. The considered problems are not convex, so local minima canbe expected.Many methods have been developed to find a local minimum of a general optimization problem. The properties of several frequently used methods are described and illustrated with a small-scale structural optimization problem. The method of coupled local minimizers, developed for global optimization, is extended for constrained optimizationproblems. The method is improved by considering a new problem formulation and parameter updating. It is concluded that this method has two important disadvantages: a careful tuning of the parameters of this method is required for every problem and the number of function evaluations needed to find the global optimum is large, even when compared to a multi-start local optimization.Optimization methods using gradient information perform significantly better. Therefore, an overview of the methods to obtain the sensitivities is presented to determine a preferred method for size and shape optimization of truss and shell structures.The geometry parameterization limits the design space and consequentlythe geometry of the final structure. Therefore, it has to be chosen carefully, especially for shell structures. In general, the geometry is parameterized using computer aided geometric design (CAGD) techniques. The resulting number of design variables is small but the design freedom is limited. In a case study, several optimizations are performed with different parameterizations. Each parameterization limits the design space insuch a way that the result of the optimization shows the effect of a single design option. Such results are useful to make a trade-off between the considered design options and relevant aesthetical or construction arguments.Alternatively, finite element (FE) based parameterization can be used. In that case, each nodal coordinate is used as design variable for shape optimization. In contrary to CAGD parameterization, this approach results in a very large design freedom withlimited modeling effort. When using the required regularization techniques, smooth appealing shapes are obtained. In this work, the FE based parameterization approach is extended for the thickness optimization of shells. Several examples illustrate the relevance of this approach. In shape as well as in thickness optimization of shell structures with FE based parameterization, the stress field can change strongly from iteration to iteration due to local shape or thickness changes. Therefore, the Kreisselmeier-Steinhauser functionis introduced to robustly constrain the stress during optimization.